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C5×Dic9×C173 #44528115

order31140
automorphism?
homologyAbelianization (H1) = C4×C5×C173 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic9×C173
unambiguous semidirect productC9⋊(C4×C5×C173)

Splittings

derived, SylowC9 ⋊ C4×C5×C173
HallC5×C9×C173 ⋊ C4
HallC9×C173 ⋊ C4×C5
HallC5×C9 ⋊ C4×C173

Subgroups

subgroupG/H
center, hypercenterC2×C5×C173D9
commutator, hypocenterC9C4×C5×C173
FrattiniC2×C3C5×D3×C173
FittingC2×C5×C9×C173C2
socle, prime radicalC2×C3×C5×C173D3
cosocleC2×C9C2×C5×C173
LCSG ▷ C9
UCSC1 ◁ C2×C5×C173

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31140

Conjugacy classes & character table

10380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31140, 5);